Springer’s relatively new Archimedes series aims at three objectives: “[t]o further the integration of the histories of science and technology with one another; to investigate the technical, social and practical histories of specific developments in science and technology; and … to bring the histories of science and technology into closer contact with the philosophy of science.” The book under review, Volume 22 in the series, is a fascinating investigation into the relations between Italy and France, and specifically between the Italian icon, Vito Volterra, and a cadre of French scholars including Emile Borel, Emile Picard, Jacques Hadamard, and, to a lesser extent, Joseph Pérès, in the context of the “war to end all war,” World War I.

While also of interest to mainstream mathematicians, modulo the proviso that they should be able to read French with some facility, the book is first of all a fine account of the effect the cataclysm of the Great War had on these representative European academics, from the inside: it is really impossible to do any better in this regard than to present the relevant correspondence. The story almost writes itself — or so it appears when the resulting book evinces the kind of seamlessness Mazliak and Tazzioli have achieved in their commentary, coming in the form of a few chapters before the Briefwechsel and a few after. The authors’ coverage of the indicated scientists’ actions and reactions concerning the war and the events and changes, proximate and more distant, that it brought about, is balanced, reasoned, and measured. Their work evinces the detachment proper to the real historian, and avoids the polemics that have become all but epidemic in this day and age when every one and his uncle has an opinion before the facts are even collected. Mathematicians at War lets Volterra, Borel, Picard, and Hadamard present their eyewitness and insider accounts, and in allowing these men to speak for themselves succeeds incomparably well in bringing today’s reader into this watershed episode of history.

So it was, then, that Volterra, a physicist and applied mathematician from the start, eventually a major player in differential equations and proto-functional analysis to boot, and the premiere Italian academician before the war, emerges as a tragic figure. Certainly he was an Italian patriot and emphatically bellicose in the face of the German enemy, and accordingly a friend and ally to the like minded French academics with whom he corresponded. But in the wake of World War I, as Italian fascism eventually took form, he showed heroism beyond measure: Volterra never wavered a millimeter in his opposition to the oncoming madness. He died in 1940, “isolated and with no official recognition,” having eight years earlier been expelled from the University of Rome. The cruel irony is amplified by the fact that twenty five years earlier, on the eve of the first World War, he had gone so far in the defense of his country as to enlist, at age 55, in the military engineers’ corps.

The authors are particularly beholden to Volterra and his estate on account of the huge and carefully arranged correspondence he scrupulously saved. The French side of the equation is by contrast more of a tapestry arrangement. But the trio of Frenchmen chosen make for good balance: there is a good flow to it all.

And there is of course a great deal of poignancy in the pages that follow the authors’ introductory sections. It is heart wrenching, for example, to read about the deaths of two of Hadamard’s sons in battle. The letters home written by the respective officers in charge (rendered in English) are exemplars of humanity and charity: the fallen men are honored for their heroism, the beauty of their souls, and for the effect they had, by virtue of their characters, on their fellows, including their commanders.

It is of course the case that the letters, in French, comprising the lion’s share of the book, deal with the matters of concern to leading academics of the indicated time and place. So it is, for example, that we find on p. 59 of the book, the following passage from Hadamard’s August 1915 letter to Volterra: “Je suis, comme vous, assez fortement occupé et de questions voisines de celles auxquelles vous vous été voué. Et comme conséquence aussi, je fais au Collège de France — je ne parle, plus, bien entendu, de l’École Polytechnique dont tous les élèves se battent et qui est convertie en hôpital — de rares cours pour de très rares élèves.” The authors add the footnote that, in point of fact, the École Polytechnique did not even open for the academic year 1914–1915; they go on to say that “[a]t the Collège de France, a considerably limited activity was maintained.” This phrase exemplifies the fact that when it comes to a cataclysm even a scholarly footnote reads like understatement.

There is also a particular horror to be read from the fact that the École Polytechnique did service as a hospital: such geographical contingencies are unimaginable to us in the vast United States, buffered west and east by oceans. The Great War was first of all fought between very proximate neighbors. A case can perhaps be made to draw a parallel of sorts with our Civil War, both for its personal cruelty and its effects on the regional players throughout subsequent history.

It is clear as a bell that Mathematicians at War: Volterra and His French Colleagues in World War I is good historical scholarship, fitting well under the rubrics of the Archimedes series. For mainstream mathematicians with an interest in historical connections, specifically the cultural roots of modern global mathematics in twentieth century Europe, the book should also serve well as a complement to Constance Reid’s Hilbert and her Courant in Göttingen and New York, Carol Ann Parikh’s biography of Zariski (The Unreal Life of Oscar Zariski), and André Weil’s idiosyncratic autobiography (The Apprenticeship of a Mathematician, a translation by Jennifer Gage of Weil’s Souvenirs d’Apprentissage). Additionally, they might read a few of the better biographies of Einstein such as the classic by Ronald W. Clark, Einstein the Life and Times, and Albrecht Fölsing’s Albert Einstein. Even though Zariski and Weil were obviously more influenced by what occurred in the wake of World War I and subsequently, certainly, World War II, it is the case that one cannot understand modern Europe, even vis à vis the narrow swath mathematics cuts out of the cultural fabric, without taking account of both wars.

Michael Berg is professor of mathematics at Loyola Marymount University in Los Angeles, CA.